In this section, we demonstrate the application of the proposed implementation of the projection filter to selected optimal filtering problems. We compare the projection filter densities against the densities obtained by solving the Zakai equation via the central finite difference approach [1]} and kernel density estimate from a bootstrap particle filter with systematic resampling [2]}. All numerical simulations in this section are implemented using JAX [3]} where the automatic differentiation is supported by default. The sparse-grid implementation is taken from the TASMANIAN library [4]}.
